Barghouthi, Imad A

Issa, Mazen S Abu

Qatanani, Naji A

IACS Institutional Repository

Indian I  Phys. 77B (6). 621-624(2003)$ IJPToroidal distributions in the polar wind plasmaIm a d  A  B a r g h o u t h i '* .  N a j i  A  Q a tanan i*  an d  M a z e n  S  A b u  Is sa 'Department of Physics, AL~Quds University, Abu-Dies, Jerusalem, Palestine Department of Mathematics, AL-Quds University, Abu-Dics, Jerusalem, PalestineE-mail barghouthi2@yahoo.comReceived 5 September 2002. accepted 30 September 2003Abstract : The energization of charged particles, due to interaction with electromagnetic turbulence, has an important influence on the plasma (uitflow in space. The effect of wave-particle interaction (WPI) on O"*^ and velocity distributions in the polar wind was investigated by using Monte Cuilo method. The Monte Carlo simulation included the effect of WPI, gravity, polarization electrostatic field, and the divergence of geomagnetic field wiihin the simulation lube (1 7-10 earth radii. Re) a.s the ions arc heated due to WPI and move to higher altitudes, the ion's Larmor radius a, may Ivcoiric comparable to the perpendicular wave length of the electromagnetic turbulence. As the ratio a/ /A j becomes > 1 , the quasi-linear ptTpfiidicular diffusion coefficient becomes velocity dependent, the healing rate becomes .self-limited and the ion ditribution displays toroidal features. This result is consistent with observations of toroidal distribution m the auroral region.Keywords - Toroidal distributions, polar wind, auroral region, Monte Carlo simulationPACS Nos. : 93.30 Sq, 94 lO.Rk, 94.20 Rr, 52.65 Pp1. IntroductionThe p o la r  w in d  is  an a m b ip o la r  o u t f lo w  o f  p la s m a  a lo n g  'o p en ' geom agnetic f ie ld  l in e s ,  it  is  w e l l  k n o w n  th a t th e  c la s s ic a l  p o la r  wind u n d e rg o e s  fo u r  m a jo r  t r a n s it io n s  in c lu d in g  a tra n s it io n  Irom c h e m ic a l to  d i f fu s io n  d o m in a n c e , a tra n s it io n  fro m  c o ll is io n  flom inated re g io n  to  c o ll is io n J e s s  r e g io n ,  an d  a t ra n s it io n  f ro m  a heavy to a l ig h t  io n  d o m in a n c e  [ 1]. In  th e  c la s s ic a l  p ic tu re  o f  the polar w in d , th e  O ’*^ io n s  a re  g r a v it a t io n a l ly  b o u n d e d , an d  the  ions are c o n t in u a l ly  b lo w n  o u t  to  h ig h e r  a lt it u d e s  w h e re  th ey  become s u p e rs o n ic  a n d  d e v e lo p  v e r y  la rg e  a n is o t ro p y  (7J| >  )|2| S e v e ra l s tu d ie s  w e re  d e v o te d  to  in c lu d e  th e  n o n - c la s s ic a l features o f  th e  p o la r  w in d .  T h e  escap je  f lu x  o f  w a s  fo u n d  to he g re a t ly  e n h a n c e d  d u e  to  e le v a te d  e le c t r o n  te m p e ra tu re , e leva ted  io n  t e m p e r a t u r e ,  a n d  e n e r g e t ic  m a g n e t o s p h e r e  electrons [ 3 ,4 ] .  W u  et, a l  [5 ] u s e d  E u r o p e a n  In c o h e re n t  S c a tte r  (KISC A T )  V H P  ra d a r  to  s tu d y  th e  v e r t ic a l f lu x  o f  an d  H"" io n sin the to p s id e  h ig h - la t i t u d e  io n o s p h e r e ;  th e y  w e re  a b le  to  determ ine th e  v e r t ic a l v e lo c i t ie s  a n d  f lu x e s  o f  th e  H ’*’ and  0 “^  ionsT h e o re t ic a l s tu d ie s  [6 ,7 ]  in d ic a te d  th a t th e  p o la r  w in d  c o u ld  I become u n s t a b le .  S i g n i f i c a n t  l e v e l s  o f  e le c t r o m a g n e t icCorresponding Author.tu rb u le n c e  w e re  o b s e rv e d , fo r  e x a m p le , b y  the p la sm a  w a v e  in s trum en t ( P W I)  aboa rd  the D y n a m ic s  E x p lo r e r  1 ( D E I )  sa te llite[8]. T h e  io n  h e a t in g  d u e  to  io n  c y c lo t r o n  re so n a n ce  w ith  th e se  tu rb u le n c e s  ha s an  im p o r ta n t  e f fe c t  o n  th e  e s ca p e  o f  th e  h e a v y  io n o s p h e r ic  io n s  in to  th e  m a g n e to sp h e re .In  a se r ie s  o f  p ape rs  [9 -1 2 ], M o n te  C a r lo  s im u la t io n  has been  used  to  in v e s t ig a te  the  e f fe c t o f  W a v e -P a r t ic le  In te ra c t io n s  (W P I )  o n  th e  0 “^  v e lo c i t y  d is t r ib u t io n  at 2  Re in  th e  a u ro ra l re g io n . T h e  m o d e l  t h e y  a d o p te d ,  ig n o r e d  th e  e f f e c t  o f  b o d y  f o r c e s  ( g ra v it a t io n a l an d  p o la r iz a t io n  e le c t ro s ta t ic )  an d  a s su m e d  an  a lt i t u d e ,  a n d  v e lo c i t y  in d e p e n d e n t  p e r p e n d ic u la r  d i f f u s io n  c o e f f ic ie n t  ) . T h e y  o b ta in e d  th e  c o n ic  d is t r ib u t io n  fo r  O**" io n s .A n o t h e r  s e r ie s  o f  p a p e rs  [ 1 3 -1 7 ] ,  u s e d  a M o n t e  C a r lo  a p p ro a ch  to  s tu d y  th e  e f fe c t  o f  w a v e -p a r t ic le  in te ra c t io n s  ( W P I )  o n  th e  an d  o u t f lo w  in  th e  p o la r  w in d  a n d  in  th e  a u ro ra l re g io n . A s  th e  io n s  d r if t  u p w a rd  a lo n g  th e  g e o m a g n e t ic  f ie ld  l in e s ,  th e y  in te ra c t  w it h  th e  e le c t r o m a g n e t ic  tu rb u le n c e  and , c o n s e q u e n t ly  ge t h e a te d  in  th e  d ir e c t io n  p e rp e n d ic u la r  to  th e  m a g n e t ic  f ie ld .  T h e  m ir r o r  fo r c e  c o n v e r t s  so m e  o f  th e  g a in e d  io n  e n e rg y  in  th e  p e rp e n d ic u la r  d ir e c t io n  in to  p a ra lle l k in e t ic  ene rgy . T h e s e  e f fe c ts  c o m b in e  to  f o rm  an  io n c o n ic  d is t r ib u t io n .  T h e y© 2 0 0 3  l A C S6222hnad A Barghouthi, Naji A Qatanani and Mazen S Abu Issain c lu d e d  th e  e f fe c t  o f  b o d y  fo r c e s  an d  an  a lt itu d e -d e p e n d e n t  p e rp e n d ic u la r  d i f f u s io n  c o e f f ic ie n t s  ) ■ T h e y  fo u n d  th e  e f fe c to f  b o d y  fo r c e s  is  m o re  im p o r ta n t  in  th e  p o la r  w in d  c a s e  a n d  fo r  0"*“ io n s  th a n  it  is  f o r  th e  a u r o r a l  r e g io n  a n d  th e  H'*’ io n s  r e s p e c t iv e ly ,  0'*’ io n s  w e re  p r e f e r e n t ia l ly  e n e r g iz e d  in  b o th  r e g io n s ,  an d  an d  w e re  e n e rg e t ic  in  th e  a u ro ra l r e g io n  at m o s t  a lt itu d e s .T h e  a b o v e  m e n t io n e d  s t u d ie s  th a t  h a n d le d  W P l ,  u s e d  R e tte re r  e t a l [ \ 2 \  fo rm  fo r  the p e rp e n d ic u la r  d if fu s io n  c o e f f ic ie n ts  Dj^ w h ic h  is  v e lo c i t y  in d e p e n d e n t , a n d  B a rg h o u th i f 17] fo rm  fo rw h ic h  is  a lt it u d e  d e p e n d e n t.In  th is  s tu d y , w e  c o m p u te d  n e w  fo rm  o f  the p e r p e n d ic u la r  d i f f u s io n  c o e f f ic ie n t s  D j  an d  w e  fo u n d  it  is  v e lo c i t y  and  a lt itu d e  d e p e n d e n t. W e  u sed  th is  n e w  Dj^ to  in v e s t ig a te  the  e f fe c t  o f  W P l  o n  th e  H'*' an d  v e lo c i t y  d is t r ib u t io n  in  th e  p o la r  w in d  p la sm a .2 . Theoretical form ulationT h e  in te ra c t io n  b e tw e e n  the  io n s  a n d  th e  e le c t r o m a g n e t ic  io n  c y c lo t r o n  w a v e s  c a n  b e  re p re s e n te d  b y  p a r t ic le  d i f f u s io n  in  th e  v e lo c i t y  sp a c e  : th a t is  ;S £St w r i ' I y C7 V I d vd f(1)w h e re  is t h e q u a s i- l in e a r v e lo c it y  d iffu .s io n  r a te p e ip e n d ic u la r  to  th e  g e o m a g n e t ic  f ie ld  l in e s .  T h e  p e r p e n d ic u la r  d i f f u s io n  ra te  f o r  r e s o n a n t  w a v e  p a r t i c le  in t e r a c t io n  w it h  a s p e c t r u m  o f  e le c t r o m a g n e t ic  tu rb u le n c e  is  g iv e n  b y  th e  f o l lo w in g  e x p re s s io n  [12]w ithA , = -^ y ,r_ ,|£ ,.f‘ (A:,a» + ^^11 JnV,\E ,\U k A O )\ k , c o ) . (3)In  th e se  e q u a t io n s , q is  th e  io n 's  c h a rg e , m is  th e  io n 's  m a ss , CO is  th e  a n g u la r  f r e q u e n c y ,  k  is  th e  w a v e  v e c to r ,  £2 is  th e  io ng y r o f r e q u e n c y ,  is  t h e  s t a n d a r d  B e s s e lfu n c t io n .  [E^|“ an d  a re  th e  s p e c t ra l d e n s it ie s  o f  th e  e le c t r ic  f ie ld  in  th e  tw o  p e r p e n d ic u la r  p o la r iz a t io n s .a n dT o  s im p l i f y  »R e t te re r  e t a l  \ 12] a s su m e d  |^|V|| «  £2,n = \k \ V \— —  «  fo u n d  th a tD =' 4m -‘ '(u) =  £2), (4)where |£ i,| ((o) = g |E , | (o)) , is ihe measured spectra)d e n s it y  o f  th e  w a v e ,  a n d  q  is  th e  p r o p o r t io n  o f  the measured s p e c t ra l d e n s it y  b y  p la s m a  w a v e  in s t r u m e n t  ( P W I )  on board D E - 1  s a t e l l it e  th a t c o r r e s p o n d s  to  a  le f t -h a n d  p o la r iz e d  waveIt is  w o r th  w h i le  to  p o in t  o u t  th a t is  spec ies-dependent s in c e  b o th  m a n d  £2  d e p e n d  o n  th e  ty p e  o f  th e  io n . R e tte re r  ei al[1 2 ] a s s u m e d  «  £2 ( i.c . the  io n  L a r m o r  ra d iu s  a to be m u c h  le s s  th a n  th e  p e r p e n d ic u la r  w a v e le n g t h  o f  the e le c t r o m a g n e t ic  tu rb u le n c e ) .  H o w e v e r ,  a s  a n  io n  d r if t s  upward a lo n g  a  g e o m a g n e t ic  f ie ld  l in e ,  i t  h e a ts  u p  d u e  to  W P J, and g e o m a g n e t ic  f ie ld  in t e n s it y  B d e c re a s e s , th e  c o m b in e d  effect ot th e se  tw o  fa c to r s  r e s u lt s  in  a r a p id  in c re a s e s  in  w ith  a lliiu d t A t  h ig h e r  a lt itu d e s , th e  L a rm o r  ra d iu s  m a y  b e co m e  comparablebecomesto  o r  e v e n  m o re  th a n  a n d  c o n s e q u e n t lyV i£2g re a te r  th a n  1, a n d  h e n c e  th e  v e lo c i t y  in d e p e n d e n t expressmn fo r  D ,  g iv e n  in  eq . (4 )  b e c o m e s  in a c c u ra te .  A t  th e se  altitudes, w e  n e ed  to  m o d if y  th e  fo rm  o f  th e  d i f f u s io n  c o e f f ic ic ( it  Ttid o  th is ,  w e  d iv id e  th e  g e n e ra l fo rm  o f  as g iv e n  in  4q. (2) h\ th e  s im p l i f ie d  fo rm  g iv e n  in  e q . (4 )  to  o b ta in  a r a t io  d cho ied  bs R :  iR =r  2  mdco f d ^ k2 k  J ( 2 k )^h QCOA^jKS^co n i2  |^|V||^i S lm "fu n c t io nW e  n o w  p lo t  th e  r a t io  R a g a in s t  th e  a rg u m e n t o f  BessdA' 1 VI— as s h o w n  in  F ig u r e  1. W h e n  the argumcni V /[ I IS le s s  th an  1, th e  r a t io  R is  o n e  w h ic h  m e an s  that D.V Q  )  _n e ed s  n o  m o d if ic a t io n ,  a n d  w e  re p ro d u c e  R e t te re r  et al |12i fo rm , b u t as th e  a rg u m e n t j b e c o m e s  g re a te r  than  J tht-nf2Figure 1. The ratio given in cq. (5) vrrsux . The straight line is jaadopted dependence of the ratio R when greater than I-£2Toroidal distributions in the po larihe ra t io  d e c re a se s  a s  j  ■ T h e r e fo r e  w h e n  > 1 w e(k V' . A s  w e  Qit I V 1m entioned  e a r lie r ,   ^ at h ig h e r  a lt itu d e s . T h e  m o d if ie dform  o f  the d i f f u s io n  c o e f f ic ie n t  is  c o n s is te n t  w ith  the suggested  form g iv e n  b y  C r e w  an d  C h a n g  [ 18J.3, Monte C arlo modelT h e  M o n te  C a r lo  m o d e l u sed  in  th is  s tu d y  is  d e s c r ib e d  in  d e ta ils  by B a rg h o u th i 117]. O n ly  a b r ie f  d e s c r ip t io n  is  g iv e n  he re  w ith  em phas is  o n  n e w  fe a tu re s  r e la t iv e  to  the m o d e l a d o p ted  in  R e fs . 111,12). W e  c o n s id e r e d  th e  s t e a d y  s ta te  f l o w  o f  a th re e  co m pon en ts  p la s m a  c o m p o s e d  o f  H'*', 0 +  an d  th e  e le c tro n s . T h e  s im u la t io n  re g io n  w a s  a g e o m a g n e t ic  tu b e  e x te n d in g  f ro m  the cxoba.se r  ^= [ J  Re to  10 /?e. T h e  io n s  w e re  in je c te d  at w ith  v e lo c ity  c o n s is te n t  w it h  a d r i f t in g  M a x w e l l i a n  d is t r ib u t io n  lun c tion . T h e  io n  m o t io n  w a s  fo l lo w e d  fo r  a 's m a ll' t im e  in te rv a l (;V) as it m o v e d  u n d e r  th e  e f fe c t  o f  g r a v it y  (g),  p o la r iz a t io n  e le c tr ic  f ie ld  (/{^), a n d  d iv e r g in g  g e o m a g n e t ic  f ie ld  B. T h e  in f lu en ce  o f  W P l  d u r in g  At w a s  s im u la te d  b y  in c r e m e n t in g  the ion 's v e lo c it y  (v ^ )  p e r p e n d ic u la r  to  b y  a r a n d o m ly  ch o se n  A \ \  [17J su ch  tha twind plasma 6 2 3( ( A v J - )  =  4 D ^ A r (6)A c c o r d in g  to  eq . (4 ), th e  d e p e n d e n c e  o f  o n  a lt itu d e  is  d u e  to  th e  d e p e n d e n c e  o f  Q  o n  a l t i t u d e .  B a r g h o u t h i  17] com pu ted  an  a lt it u d e  d e p e n d e n c e  fo rm  fo r  b y  a n a ly z in g  e x p e r im e n ta l d a ta  c o lle c t e d  b y  P W l  in s t ru m e n t o n  b o a rd  D E - J  sa te llite . In  th is  p ap e r, w e  u sed  f r o m  B a rg h o u th i [ 1 7 1 i.e.D j  ( / y “* ) [ t7 / r  s e c  jD j^ ( 0 * ) [ fm - s e c '^ ]  = 9 .5 5 x 1 0 ^(7)(8)In  F ig u r e  2 , the  to p  p a n e l s h o w s  th e  v e lo c i t y  d is t r ib u t io n  and  th e  b o t to m  p a n e l s h o w s  th e  v e lo c i t y  d is t r ib u t io n  at 10  Re fo r  A   ^ = 1 k m . A t  h ig h  a lt itu d e s , the d is t r ib u t io n  fu n c t io n  d is p la y s  to r o id a l fe a tu re s . T h is  to ro id a l sh ap e  c a n  b eIc Ve x p la in e d  i f  w e  re m e m b e r  that p e a k s  n e a r  ^ « 1  an dit  V' ^d e c re a se s  r a p id ly  fo r  la rg e  v a lu e s  o f  as s h o w n  in  F ig u r e  1 .1  h e re fo re  the io n s  le n d  to  m o v e  o u t o f  th e  re g io n  o f  la rg ed i f f u s io n  (A j  < l )  a n d  a c c u m u la t e  in  th e  r e g io n  o fr e la t iv e ly  lo w  , k^Vj^ l£2>\  f o rm in g  th e  a fo re m e n t io n e d  t o r o id a l  d is t r ib u t io n s .  T h e  t o r o id a l  f e a t u r e s  f o r  O'*’ io n  d is tr ib u t io n  appea r e a r lie r  at 4 .3  Re, and  th ey  are w e ll p n m o u n ce d  at 10 Re. H o w e v e r ,  H*** to ro id a l fe a tu re s  a p p ea r at 10 R^^The O'*' io n s  are  hea ted  m o re  e f f ic ie n t ly  th an  H"*^  io n s , e s p e c ia l ly  at lo wk Va lt itu d e s  d u e  to p re ssu re  c o o k e r  e f fe c t 1131. T h e  a rg u m en t a p p ro a ch e s  1 fo r  0 '* 'faster th an  F H , c o n s e q u e n t ly , O'** io n s  ge t h ea ted  b e fo re  H'*' io n s  an d  th e ir  to ro id a l fe a tu re s  a p p e a r at lo w  a lt itu d e . In  an o n -g o in g  s tu dy , the a b o v e  m e ch a n ism  m a y  be th e  f ir s t  th e o re t ic a l e x p la n a t io n  o f  the O*' to ro id a l o b s e rv a t io n s  in  the  au ro ra l re g io n  [ 1 9 1.k Vand w h e n e v e r  > 1 , w e  m u lt ip l ie d  th e  a b o v e  a lt i t u d edependen t b y  its  v e lo c i t y  d e p e n d e n c e  " "In  the  s im u la t io n ,  a la rg e  n u m b e r  o f  te s t io n s  (10^) w e re  fo l lo w e d  (o n e  at a t im e )  as  th e y  m o v e d  u n t i l  th e y  e x it  th e  s im u la t io n  re g io n . T h e  O ’*" a n d  H"*" v e lo c i t y  d is t r ib u t io n  fu n c t io n s  w ere c o m p u te d  a t d i f f e r e n t  a lt itu d e s . S in c e  th e  d a ta  c o lle c te d  by the P W I  d o  n o t in c lu d e  in fo rm a t io n  ab o u t . W e  co n s id e re d  a w id e  ra n g e  ( A ^  = 1. 10, 1 0 0  k m )  th a t c o v e r s  th e  c o n d it io n : , e xp ec ted  to  o c c u r  a b o v e  th e  p o la r  cap .4. R e s u lt sN o w , w e  re p o r t th e  e f fe c t  o f  s e l f - l im i t in g  h e a t in g  o n  O'*’ and  H"*.Figure 2. The top panel shows Ihe velocity distribution f{0 *) and the bottom panel shows the IP  velocity distribution ,/\IP ) at 10 /fr for the electromagnetic turbulence wavelength -  1 km andA^^)reprc.scntcd by equal-value contours in the normalized vclocity(vj|, plane, whereV U r ) = [V( H* )]/[2A,T( I I  * )/m {H * )]''^andV (0*) = [v (0 ^  )] /[2 m o *  )/m{0*The contour levels decrease successively by a facior e*'* from the maximum (marked by dot).624 Imad A Barghouthi, Naji A Qatanani and Mazen S Abu Issa5. ConciiisionIn conclusion, the effect of self-limiting heating on/(H*) and fiP * )  velocity distribution functions was studied for conditions representative of the polar wind. We used the Monte Carlo simulation for polar wind, m addition to WPI, we considered the body forces (gravitational and polarization electrostatic) and the divergence of geomagnetic field [ 17]. As the ions were heated at high altitudes, their gyro-radius increases and exceeds the wavelength of the electromagnetic turbulence. This result in a vekxity and altitude-dependent quasi-linear perpendicular diffusion coefficient . The effect of the above phenomena ii.e. self-limiting heating) was investigated at 10/?e and for = 1km. Finally, we have illustrated the process of toroidal formation through self-limiting heating by electromagnetic turbulence (Aj^  = 1 km), We explicitly considered H* and O'^  ions in the calculations presented here.References[I I A Barghouthi, V Pierrard, A R Barakat and J Lcmairc A.stropim. Space Sii. 277 427 (2001), R W Schunk P>iy.\. Space Plasm 8 81 (1980), J Lemaire and V Pierrard Asirophys. Spare Sri. I l l  169 (2001)|2| A R Barakat and R W .Schunk J Geoplm Res 88 7887 (1983)[3] A R Barakat and R W Schunk /  Geophys Res 89 9771 (1984)[4] P Li, G R Wilson, J L Horwitz and T B Moore Gec^ hys9753 (1988) '[5] J Wu, M Blanc, D Alcayde, A R Barakat, J Fonlanari, P L Blelland W Kofman Ann. Geophys. 10 375 (1992) ^[6] A R Barakat and R W Schunk J. Geophys. Res. 94 1487 (i9g9^[7] MW Chen and M Ashour-abdalla J. Geophys. Res. 95 ii;i)49 (1990)[8] D A Gumett and U S Inan Rev. Geophys. 26 285 (1988)[9] J M Rcttcrer, T Chang and J R Jasperse Geophy.s. Res Lett to 583 (1983)[10] J M Retterer, T C^ng and J R Jasperse J. Gec^ hys. Res 91 icoq (1986)[11] J M Rcttcrcr, T Chang, G D Crew, J R jasperse and J D Winningham Phys Rev Ult. 59 148 (1987)[12] J M Retterer. 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Toroidal Distributions in the Polar Wind Plasma

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Toroidal Distributions in the Polar Wind Plasma

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